36 The Quantum Structure of Space and Tame
0 Every fine-grained history of the effective theory is a coarse-grained history of
The decoherence functionals approximately agree on a limited class of sets of
the fundamental theory.coarse-grained histories.Dfund(al, a) M Deff(Q1, a). (16)
On the right, a' and Q refer to the fine-grained histories of the effective the-
ory. On the left, they refer to the corresponding coarse-grained histories of the
fundamental theory.When two theories are related in this way we can say that the effective theory is
emergent from the fundamental theory. Loosely we can say that the restrictions, and
the concepts that characterize them, are emergent. It should be emphasized that an
approximate equality like (16) can be expected to hold, not just as a consequence
of the particular dynamics incorporated into decoherence functionals, but also only
for particular states.
Several examples of emergence in this sense have been considered in this essay:
There is the possible emergence of a generalized quantum theory of spacetime geom-
etry from a theory in which spacetime is not fundamental. There is the emergence
of a 3+1 quantum theory of fields in a fixed background geometry from a four-
dimensional generalized quantum theory in which geometry is a quantum variable.
There is the emergence of the approximate quantum mechanics of measured sub-
systems (textbook quantum theory) from the quantum mechanics of the universe.
And there is the emergence of classical physics from quantum physics.
Instead of looking at an effective theory as a restriction of a more fundamental
one, we may look at the fundamental theory as a generalization of the effective one.
That perspective is important because generalization is a way of searching for more
comprehensive theories of nature. In passing from the specific to the more general
some ideas have to be discarded. They are often ideas that were once perceived to
be general because of our special place in the universe and the limited range of our
experience. But, in fact, they arise from special situations in a more general theory.
They are 'excess baggage' that has to be discarded to reach a more comprehensive
theory [53]. Emergence and excess baggage are two ways of looking at the same
thing.
Physics is replete with examples of emergence and excess baggage ranging from
Earth-centered theories of the solar system to quantum electrodynamics. The chart
on the next page helps understand the stages of emergence and generalization in
quantum mechanics discussed in this essay provided it is not taken too rigidly or
without qualification.